
Basic Algebraic Operations 


1  (49) 


2  (4) 

Fundamental Operations of Algebra 


6  (5) 

Calculators and Approximate Numbers 


11  (5) 


16  (5) 


21  (3) 


24  (2) 

Addition and Subtraction of Algebraic Expressions 


26  (4) 

Multiplication of Algebraic Expressions 


30  (2) 

Division of Algebraic Expressions 


32  (4) 


36  (3) 

Formulas and Literal Equations 


39  (3) 


42  (8) 

Chapter Equations, Review Exercises, and Practice Test 


46  (4) 


50  (31) 


51  (3) 


54  (7) 


61  (3) 


64  (4) 

Measurement of Irregular Areas 


68  (4) 


72  (9) 

Chapter Equations, Review Exercises, and Practice Test 


76  (5) 


81  (29) 

Introduction to Functions 


82  (3) 


85  (5) 


90  (2) 


92  (6) 

Graphs on the Graphing Calculator 


98  (5) 

Graphs of Functions Defined by Tables of Data 


103  (7) 

Review Exercises and Practice Test 


107  (3) 

The Trigonometric Functions 


110  (27) 


111  (3) 

Defining the Trigonometric Functions 


114  (4) 

Values of the Trigonometric Functions 


118  (4) 


122  (5) 

Applications of Right Triangles 


127  (10) 

Chapter Equations, Review Exercises, and Practice Test 


132  (5) 

Systems of Linear Equations; Determinants 


137  (39) 


138  (3) 

Graphs of Linear Functions 


141  (4) 

Solving Systems of Two Linear Equations in Two Unknowns Graphically 


145  (4) 

Solving Systems of Two Linear Equations in Two Unknowns Algebraically 


149  (7) 

Solving Systems of Two Linear Equations in Two Unknowns by Determinants 


156  (5) 

Solving Systems of Three Linear Equations in Three Unknowns Algebraically 


161  (5) 

Solving Systems of Three Linear Equations in Three Unknowns by Determinants 


166  (10) 

Chapter Equations, Review Exercises, and Practice Test 


171  (5) 


176  (40) 


177  (3) 

Factoring: Common Factor and Difference of Squares 


180  (5) 


185  (6) 

The Sum and Differences of Cubes 


191  (2) 


193  (5) 

Multiplication and Division of Fractions 


198  (4) 

Addition and Subtraction of Fractions 


202  (6) 

Equations Involving Fractions 


208  (8) 

Chapter Equations, Review Exercises, and Practice Test 


212  (4) 


216  (19) 

Quadratic Equations; Solution by Factoring 


217  (4) 


221  (3) 


224  (4) 

The Graph of the Quadratic Function 


228  (7) 

Chapter Equations, Review Exercises, and Practice Test 


232  (3) 

Trigonometric Functions of Any Angle 


235  (23) 

Signs of the Trigonometric Functions 


236  (2) 

Trigonometric Functions of Any Angle 


238  (6) 


244  (5) 

Applications of Radian Measure 


249  (9) 

Chapter Equations, Review Exercises, and Practice Test 


254  (4) 

Vectors and Oblique Triangles 


258  (34) 


259  (4) 


263  (4) 

Vector Addition by Components 


267  (5) 


272  (5) 

Oblique Triangles, the Law of Sines 


277  (7) 


284  (8) 

Chapter Equations, Review Exercises, and Practice Test 


289  (3) 

Graphs of the Trigonometric Functions 


292  (25) 

Graphs of y = a sin x and y = a cos x 


293  (3) 

Graphs of y = a sin bx and y = a cos bx 


296  (4) 

Graphs of y = a sin(bx + c) and y = a cos(bx + c) 


300  (3) 

Graphs of y = tan x, y = cot x, y = sec x, y = csc x 


303  (3) 

Applications of the Trigonometric Graphs 


306  (3) 

Composite Trigonometric Curves 


309  (8) 

Chapter Equations, Review Exercises, and Practice Test 


313  (4) 


317  (22) 

Simplifying Expressions with Integral Exponents 


318  (4) 


322  (5) 


327  (3) 

Addition and Subtraction of Radicals 


330  (3) 

Multiplication and Division of Radicals 


333  (6) 

Chapter Equations, Review Exercises, and Practice Test 


337  (2) 


339  (31) 


340  (3) 

Basic Operations with Complex Numbers 


343  (3) 

Graphical Representation of Complex Numbers 


346  (3) 

Polar Form of a Complex Number 


349  (3) 

Exponential Form of a Complex Number 


352  (3) 

Products, Quotients, Powers, and Roots of Complex Numbers 


355  (6) 

An Application to AlternatingCurrent (ac) Circuits 


361  (9) 

Chapter Equations, Review Exercises, and Practice Test 


367  (3) 

Exponential and Logarithmic Functions 


370  (29) 


371  (2) 


373  (4) 


377  (5) 

Logarithms to the Base 10 


382  (3) 


385  (3) 

Exponential and Logarithmic Equations 


388  (4) 

Graphs on Logarithmic and Semilogarithmic Paper 


392  (7) 

Chapter Equations, Review Exercises, and Practice Test 


396  (3) 

Additional Types of Equations and Systems of Equations 


399  (17) 

Graphical Solution of Systems of Equations 


400  (3) 

Algebraic Solution of Systems of Equations 


403  (4) 

Equations in Quadratic Form 


407  (3) 


410  (6) 

Review Exercises and Practice Test 


414  (2) 

Equations of Higher Degree 


416  (19) 

The Remainder and Factor Theorems; Synthetic Division 


417  (5) 


422  (5) 

Rational and Irrational Roots 


427  (8) 

Chapter Equations, Review Exercises, and Practice Test 


433  (2) 


435  (23) 

Definitions and Basic Operations 


436  (4) 

Multiplication of Matrices 


440  (5) 

Finding the Inverse of a Matrix 


445  (5) 

Matrices and Linear Equations 


450  (8) 

Chapter Equations, Review Exercises, and Practice Test 


454  (4) 


458  (30) 

Properties of Inequalities 


459  (4) 

Solving Linear Inequalities 


463  (5) 

Solving Nonlinear Inequalities 


468  (7) 

Inequalities Involving Absolute Values 


475  (3) 

Graphical Solution of Inequalities with Two Variables 


478  (3) 


481  (7) 

Chapter Equations, Review Exercises, and Practice Test 


485  (3) 


488  (15) 


489  (4) 


493  (10) 

Chapter Equations, Review Exercises, and Practice Test 


499  (4) 

Sequences and the Binomial Theorem 


503  (21) 


504  (5) 


509  (4) 

Infinite Geometric Series 


513  (3) 


516  (8) 

Chapter Equations, Review Exercises, and Practice Test 


521  (3) 

Additional Topics in Trigonometry 


524  (35) 

Fundamental Trigonometric Identities 


525  (7) 

The Sum and Difference Formulas 


532  (5) 


537  (4) 


541  (3) 

Solving Trigonometric Equations 


544  (5) 

The Inverse Trigonometric Functions 


549  (10) 

Chapter Equations, Review Exercises, and Practice Test 


555  (4) 


559  (49) 


560  (4) 


564  (6) 


570  (4) 


574  (5) 


579  (5) 


584  (6) 


590  (3) 

The SecondDegree Equation 


593  (3) 


596  (4) 

Curves in Polar Coordinates 


600  (8) 

Chapter Equations, Review Exercises, and Practice Test 


603  (5) 

Introduction to Statistics 


608  (37) 


609  (4) 

Measures of Central Tendency 


613  (4) 


617  (4) 


621  (6) 

Statistical Process Control 


627  (5) 


632  (5) 


637  (8) 

Chapter Equations, Review Exercises, and Practice Test 


641  (4) 


645  (46) 


646  (8) 

The Slope of a Tangent to a Curve 


654  (3) 


657  (4) 

The Derivative as an Instantaneous Rate of Change 


661  (4) 

Derivatives of Polynomials 


665  (5) 

Derivatives of Products and Quotients of Functions 


670  (5) 

The Derivative of a Power of a Function 


675  (6) 

Differentiation of Implicit Functions 


681  (2) 


683  (8) 

Chapter Equations, Review Exercises, and Practice Test 


687  (4) 

Applications of the Derivative 


691  (42) 


692  (3) 

Newton's Method for Solving Equations 


695  (3) 


698  (5) 


703  (4) 

Using Derivatives in Curve Sketching 


707  (6) 


713  (5) 

Applied Maximum and Minimum Problems 


718  (7) 

Differentials and Linear Approximations 


725  (8) 

Chapter Equations, Review Exercises, and Practice Test 


729  (4) 


733  (25) 


734  (2) 


736  (5) 


741  (5) 


746  (3) 

Numerical Integration: The Trapezoidal Rule 


749  (3) 


752  (6) 

Chapter Equations, Review Exercises, and Practice Test 


755  (3) 

Applications of Integration 


758  (39) 

Applications of the Indefinite Integral 


759  (5) 


764  (6) 


770  (5) 


775  (7) 


782  (5) 


787  (10) 

Chapter Equations, Review Exercises, and Practice Test 


792  (5) 

Differentiation of Transcendental Functions 


797  (34) 

Derivatives of the Sine and Cosine Functions 


798  (5) 

Derivatives of the Other Trigonometric Functions 


803  (3) 

Derivatives of the Inverse Trigonometric Functions 


806  (4) 


810  (5) 

Derivative of the Logarithmic Function 


815  (4) 

Derivative of the Exponential Function 


819  (4) 


823  (8) 

Chapter Equations, Review Exercises, and Practice Test 


827  (4) 


831  (44) 

The General Power Formula 


832  (2) 

The Basic Logarithmic Form 


834  (4) 


838  (3) 

Basic Trigonometric Forms 


841  (4) 

Other Trigonometric Forms 


845  (4) 

Inverse Trigonometric Forms 


849  (4) 


853  (3) 

Integration by Trigonometric Substitution 


856  (3) 

Integration by Partial Fractions: Nonrepeated Linear Factors 


859  (4) 

Integration by Partial Fractions: Other Cases 


863  (5) 

Integration by Use of Tables 


868  (7) 

Chapter Equations, Review Exercises, and Practice Test 


871  (4) 

Expansion of Functions in Series 


875  (35) 


876  (4) 


880  (4) 

Certain Operations with Series 


884  (4) 

Computations by Use of Series Expansions 


888  (3) 


891  (3) 

Introduction to Fourier Series 


894  (7) 

More about Fourier Series 


901  (9) 

Chapter Equations, Review Exercises, and Practice Test 


906  (4) 


910  (51) 

Solutions of Differential Equations 


911  (2) 


913  (4) 


917  (2) 

The Linear Differential Equation of the First Order 


919  (3) 


922  (6) 

HigherOrder Homogeneous Equations 


928  (4) 

Auxiliary Equations with Repeated or Complex Roots 


932  (3) 

Solutions of Nonhomogeneous Equations 


935  (5) 

Applications of HigherOrder Equations 


940  (7) 


947  (5) 

Solving Differential Equations by Laplace Transforms 


952  (9) 

Chapter Equations, Review Exercises, and Practice Test 


956  (5) 


961  

HigherOrder Determinants 


961  (6) 


967  (3) 


970  (4) 

Functions of Two Variables 


974  (3) 

Curves and Surfaces in Three Dimensions 


977  (6) 


983  (4) 


987  (4) 

Numerical Solutions of Differential Equations 


991  


1  (3) 


1  (1) 

A.2 Suggestions for Study 


2  (1) 

A.3 Solving Word Problems 


3  (1) 

Appendix B Units of Measurement; The Metric System 


4  (6) 


4  (3) 

B.2 Reductions and Conversions 


7  (3) 

Appendix C The Graphing Calculator 


10  (8) 


10  (1) 

C.2 The Graphing Calculator 


10  (4) 

C.3 Graphing Calculator Programs 


14  (4) 

Appendix D Newton's Method 


18  (1) 

Appendix E Table of Integrals 


19  
Answers to OddNumbered Exercises 

1  (1) 
Solutions to Practice Test Problems 

1  (1) 
Index of Applications 

1  (10) 
Index of Writing Exercises 

11  (2) 
Index 

13  